Metrics for Numeric.SpecFunctions:logGammaCorrection from math-functions-0.1.5.2

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
100%	100%	0%	0%	0%	0%	0%	1

Compiler

Compiled 9 to 7 computations (22.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

ival-sub: 0.0ms (0% of total)

ival-mult: 0.0ms (0% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample644.0ms (25.4%)

Results

457.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 277.0ms

ival-mult: 196.0ms (70.7% of total)

ival-sub: 65.0ms (23.5% of total)

const: 14.0ms (5.1% of total)

backward-pass: 2.0ms (0.7% of total)

Bogosity

preprocess17.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

40×	`distribute-lft-neg-in`
36×	`associate-r`
32×	`associate-l`
26×	`sub-neg`
26×	`distribute-rgt-neg-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	30	22
2	78	21
3	176	21
4	255	21
5	282	21
6	286	21
0	6	7
1	14	7
2	18	7
0	18	6

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(- (* (* x x) 2) 1)

Outputs
(- (* (* x x) 2) 1)
(+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal -1 binary64))

Call 2

Inputs
(- (* (* x x) 2) 1)
(- (* (* (neg x) (neg x)) 2) 1)
(neg (- (* (* (neg x) (neg x)) 2) 1))

Outputs
(- (* (* x x) 2) 1)
(+ (* x (* x 2)) -1)
(- (* (* (neg x) (neg x)) 2) 1)
(+ (* x (* x 2)) -1)
(neg (- (* (* (neg x) (neg x)) 2) 1))
(+ 1 (* (* x x) -2))

Symmetry

(abs x)

explain61.0ms (2.4%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`(.f64 (.f64 x x) #s(literal 2 binary64))`
-	-	`(*.f64 x x)`
-	-	`#s(literal 1 binary64)`
-	-	`#s(literal 2 binary64)`
-	-	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`

Results

37.0ms

512×

valid

Compiler

Compiled 48 to 28 computations (41.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-mult: 12.0ms (71.2% of total)

ival-sub: 3.0ms (17.8% of total)

const: 2.0ms (11.9% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

Compiler

Compiled 8 to 6 computations (25% saved)

localize37.0ms (1.5%)

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) #s(literal 2 binary64))
✓	cost-diff	0	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
✓	accuracy	100.0%	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 (.f64 x x) #s(literal 2 binary64))

Rules

14×	`-lowering-.f32`
14×	`-lowering-.f64`
8×	`accelerator-lowering-fma.f32`
8×	`accelerator-lowering-fma.f64`
6×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
1	14	18
2	18	18
0	18	17

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(- (* (* x x) 2) 1)
(* (* x x) 2)
(* x x)
x
2
1

Outputs
(- (* (* x x) 2) 1)
(+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal -1 binary64))
(* (* x x) 2)
(.f64 (.f64 x x) #s(literal 2 binary64))
(* x x)
(*.f64 x x)
x
2
#s(literal 2 binary64)
1
#s(literal 1 binary64)

Results

18.0ms

256×

valid

Compiler

Compiled 20 to 11 computations (45% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-mult: 7.0ms (76.9% of total)

ival-sub: 1.0ms (11% of total)

const: 1.0ms (11% of total)

backward-pass: 0.0ms (0% of total)

series4.0ms (0.2%)

Counts

3 → 36

Calls

Call 1

Inputs
#<alt (* (* x x) 2)>
#<alt (* x x)>
#<alt (- (* (* x x) 2) 1)>

Outputs
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt -1>
#<alt (- (* 2 (pow x 2)) 1)>
#<alt (- (* 2 (pow x 2)) 1)>
#<alt (- (* 2 (pow x 2)) 1)>
#<alt (* 2 (pow x 2))>
#<alt (* (pow x 2) (- 2 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 2 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 2 (/ 1 (pow x 2))))>
#<alt (* 2 (pow x 2))>
#<alt (* (pow x 2) (- 2 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 2 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- 2 (/ 1 (pow x 2))))>

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(* (* x x) 2)
0.0ms	x	@	inf	(* x x)
0.0ms	x	@	inf	(* (* x x) 2)
0.0ms	x	@	inf	(- (* (* x x) 2) 1)
0.0ms	x	@	0	(- (* (* x x) 2) 1)

rewrite824.0ms (32.5%)

Algorithm

1×	batch-egg-rewrite

Rules

12208×	`accelerator-lowering-fma.f32`
12208×	`accelerator-lowering-fma.f64`
3996×	`-lowering-.f32`
3996×	`-lowering-.f64`
3976×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	28	15
2	170	15
3	1565	15
0	8550	14

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 244

Calls

Call 1

Inputs
(* (* x x) 2)
(* x x)
(- (* (* x x) 2) 1)

Outputs
(exp.f64 (log.f64 (.f64 (.f64 x x) #s(literal 2 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 x x) #s(literal 2 binary64))) #s(literal 1 binary64)))
(/.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 x x) #s(literal -2 binary64)) #s(literal -1 binary64))
(pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(.f64 x (.f64 x #s(literal 2 binary64)))
(.f64 x (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1 binary64)))
(.f64 x (exp.f64 (log.f64 (.f64 x #s(literal 2 binary64)))))
(.f64 (.f64 x x) #s(literal 2 binary64))
(.f64 (.f64 x x) (exp.f64 (log.f64 #s(literal 2 binary64))))
(.f64 #s(literal 2 binary64) (.f64 x x))
(.f64 (.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 2 binary64)))
(.f64 (.f64 x #s(literal 2 binary64)) x)
(.f64 (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 1 binary64)) x)
(.f64 (exp.f64 (log.f64 (.f64 x #s(literal 2 binary64)))) x)
(.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (.f64 x x))
(.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(/.f64 (*.f64 x x) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) #s(literal -1 binary64))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(*.f64 x x)
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x x))
(+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal 2 binary64)))
(+.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))))))
(+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 #s(literal 4 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) #s(literal -1 binary64)))
(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 #s(literal 4 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal 2 binary64)))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (-.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal 2 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) #s(literal 1 binary64)))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) #s(literal 512 binary64)) (+.f64 (+.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 64 binary64)) #s(literal 1 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 64 binary64)) #s(literal 1 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 64 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (.f64 (.f64 x x) #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (.f64 (.f64 x x) #s(literal 2 binary64))))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) #s(literal 512 binary64)) (+.f64 (+.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 64 binary64)) #s(literal 1 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (.f64 (.f64 x x) #s(literal 2 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 64 binary64)) #s(literal 1 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (.f64 (.f64 x x) #s(literal 2 binary64))))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 64 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (.f64 (.f64 x x) #s(literal 2 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (.f64 (.f64 x x) #s(literal 2 binary64))))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 64 binary64)) (+.f64 (.f64 #s(literal 16 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64))))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 16 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64))))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))))
(-.f64 (/.f64 (/.f64 (.f64 #s(literal 16 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 (-.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal 2 binary64))) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)))) (-.f64 #s(literal 0 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))))
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(.f64 (+.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 64 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)) (+.f64 (.f64 #s(literal 16 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)))))))
(.f64 (+.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 64 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))))))
(.f64 (+.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 64 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 #s(literal 16 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -4 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (.f64 (*.f64 x x) #s(literal 2 binary64)))))
(.f64 (+.f64 (.f64 #s(literal 16 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64))))))
(.f64 (+.f64 (.f64 #s(literal 16 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (-.f64 (-.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal 2 binary64))) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))))))
(.f64 (+.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) (-.f64 #s(literal -1 binary64) (.f64 (.f64 x x) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)) (+.f64 (.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (.f64 #s(literal 64 binary64) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))))))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 64 binary64) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))))) (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (/.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))))))))
(.f64 (-.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 64 binary64)) (.f64 (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 16 binary64)) (.f64 (/.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) (/.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))))) (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 #s(literal 4 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (+.f64 (.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))))))
(.f64 (-.f64 (.f64 #s(literal 64 binary64) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))))))
(.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 16 binary64)) (.f64 (/.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) (/.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64))) (+.f64 (.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) #s(literal 512 binary64)) #s(literal -1 binary64)) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 64 binary64)) #s(literal 1 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 8 binary64))))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 64 binary64)) #s(literal -1 binary64)) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 8 binary64))))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 64 binary64)) #s(literal -1 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 16 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal 4 binary64))))))
(.f64 (/.f64 (+.f64 (.f64 #s(literal 16 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x)))) #s(literal -1 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal 4 binary64)))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) #s(literal -1 binary64)) (+.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 64 binary64)) (.f64 (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)))))) (+.f64 (.f64 #s(literal 16 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x)))) (.f64 (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64))))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) #s(literal -1 binary64)) (.f64 (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) (+.f64 (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -2 binary64))) #s(literal -1 binary64)))) (+.f64 (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) #s(literal -2 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 (.f64 (*.f64 x x) #s(literal 4 binary64)) #s(literal -2 binary64)))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -4 binary64) (.f64 (.f64 x x) (.f64 x x))))) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 2 binary64))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)) (+.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 64 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 16 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal 4 binary64))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64)) (+.f64 (.f64 #s(literal 16 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x)))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal 4 binary64)))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) (+.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) #s(literal 512 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 64 binary64)) #s(literal 1 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 8 binary64))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) (+.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 64 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 8 binary64))))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))) #s(literal -1/2 binary64)))

simplify324.0ms (12.8%)

Algorithm

1×	egg-herbie

Rules

4322×	`-lowering-.f32`
4322×	`-lowering-.f64`
2742×	`accelerator-lowering-fma.f32`
2742×	`accelerator-lowering-fma.f64`
1586×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	170
1	19	170
2	40	170
3	85	170
4	201	170
5	342	170
6	840	170
7	2294	170
8	3210	170
9	5524	170
0	8307	161

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

Inputs
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
-1
(- (* 2 (pow x 2)) 1)
(- (* 2 (pow x 2)) 1)
(- (* 2 (pow x 2)) 1)
(* 2 (pow x 2))
(* (pow x 2) (- 2 (/ 1 (pow x 2))))
(* (pow x 2) (- 2 (/ 1 (pow x 2))))
(* (pow x 2) (- 2 (/ 1 (pow x 2))))
(* 2 (pow x 2))
(* (pow x 2) (- 2 (/ 1 (pow x 2))))
(* (pow x 2) (- 2 (/ 1 (pow x 2))))
(* (pow x 2) (- 2 (/ 1 (pow x 2))))

Outputs
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
-1
#s(literal -1 binary64)
(- (* 2 (pow x 2)) 1)
(+.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64))
(- (* 2 (pow x 2)) 1)
(+.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64))
(- (* 2 (pow x 2)) 1)
(+.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* (pow x 2) (- 2 (/ 1 (pow x 2))))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64))
(* (pow x 2) (- 2 (/ 1 (pow x 2))))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64))
(* (pow x 2) (- 2 (/ 1 (pow x 2))))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* (pow x 2) (- 2 (/ 1 (pow x 2))))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64))
(* (pow x 2) (- 2 (/ 1 (pow x 2))))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64))
(* (pow x 2) (- 2 (/ 1 (pow x 2))))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal -1 binary64))

eval102.0ms (4%)

Compiler: Compiled 14058 to 5799 computations (58.7% saved)

prune85.0ms (3.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	278	2	280
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	278	3	281

Accuracy

100.0%

Counts

281 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
▶	48.8%	(.f64 #s(literal 2 binary64) (.f64 x x))
▶	52.3%	#s(literal -1 binary64)

Compiler

Compiled 16 to 12 computations (25% saved)

localize36.0ms (1.4%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 x x))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 #s(literal 2 binary64) (.f64 x x))

Rules

14×	`-lowering-.f32`
14×	`-lowering-.f64`
6×	`*-commutative`
2×	`associate-r`
2×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	8	11
2	11	11
0	11	11

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
-1
(* 2 (* x x))
2
(* x x)
x

Outputs
-1
#s(literal -1 binary64)
(* 2 (* x x))
(.f64 x (.f64 #s(literal 2 binary64) x))
2
#s(literal 2 binary64)
(* x x)
(*.f64 x x)
x

Results

17.0ms

256×

valid

Compiler

Compiled 13 to 7 computations (46.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-mult: 4.0ms (86.9% of total)

const: 1.0ms (21.7% of total)

backward-pass: 0.0ms (0% of total)

series2.0ms (0.1%)

Counts

2 → 24

Calls

Call 1

Inputs
#<alt (* 2 (* x x))>
#<alt (* x x)>

Outputs
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(* 2 (* x x))
0.0ms	x	@	inf	(* 2 (* x x))
0.0ms	x	@	-inf	(* 2 (* x x))
0.0ms	x	@	0	(* x x)
0.0ms	x	@	inf	(* x x)

rewrite250.0ms (9.8%)

Algorithm

1×	batch-egg-rewrite

Rules

2136×	`pow-lowering-pow.f64`
2136×	`pow-lowering-pow.f32`
1588×	`-lowering-.f32`
1588×	`-lowering-.f64`
1412×	`prod-exp`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	4	8
1	8	8
2	18	8
3	34	8
4	90	8
5	282	2
6	1655	2
7	1680	2
8	1803	2
9	3052	2
0	8395	2

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 3

Calls

Call 1

Inputs
(* 2 (* x x))
(* x x)

Outputs
#s(literal 2 binary64)
#s(literal 1 binary64)
x

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

14×	`-lowering-.f32`
14×	`-lowering-.f64`
6×	`*-commutative`
2×	`pow-lowering-pow.f64`
2×	`pow-lowering-pow.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	96
1	6	96
2	10	96
3	11	96
0	11	96

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 24

Calls

Call 1

Inputs
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
(* 2 (pow x 2))
(.f64 x (.f64 #s(literal 2 binary64) x))
(* 2 (pow x 2))
(.f64 x (.f64 #s(literal 2 binary64) x))
(* 2 (pow x 2))
(.f64 x (.f64 #s(literal 2 binary64) x))
(* 2 (pow x 2))
(.f64 x (.f64 #s(literal 2 binary64) x))
(* 2 (pow x 2))
(.f64 x (.f64 #s(literal 2 binary64) x))
(* 2 (pow x 2))
(.f64 x (.f64 #s(literal 2 binary64) x))
(* 2 (pow x 2))
(.f64 x (.f64 #s(literal 2 binary64) x))
(* 2 (pow x 2))
(.f64 x (.f64 #s(literal 2 binary64) x))
(* 2 (pow x 2))
(.f64 x (.f64 #s(literal 2 binary64) x))
(* 2 (pow x 2))
(.f64 x (.f64 #s(literal 2 binary64) x))
(* 2 (pow x 2))
(.f64 x (.f64 #s(literal 2 binary64) x))
(* 2 (pow x 2))
(.f64 x (.f64 #s(literal 2 binary64) x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

eval3.0ms (0.1%)

Compiler: Compiled 128 to 68 computations (46.9% saved)

prune13.0ms (0.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	25	2	27
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	25	5	30

Accuracy

100.0%

Counts

30 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
✓	48.8%	(.f64 #s(literal 2 binary64) (.f64 x x))
▶	4.3%	(*.f64 #s(literal 2 binary64) x)
▶	2.8%	#s(literal 2 binary64)
✓	52.3%	#s(literal -1 binary64)

Compiler

Compiled 22 to 17 computations (22.7% saved)

localize23.0ms (0.9%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) x)

Rules

4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	5
1	4	5
0	4	5

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
2
(* 2 x)
x

Outputs
2
#s(literal 2 binary64)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
x

Results

10.0ms

256×

valid

Compiler

Compiled 8 to 6 computations (25% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-mult: 2.0ms (75.3% of total)

const: 1.0ms (37.7% of total)

backward-pass: 0.0ms (0% of total)

series3.0ms (0.1%)

Counts

1 → 12

Calls

Call 1

Inputs
#<alt (* 2 x)>

Outputs
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(* 2 x)
1.0ms	x	@	-inf	(* 2 x)
0.0ms	x	@	0	(* 2 x)

rewrite8.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
1	4	3
0	4	3

Stop Event

1×	iter limit
1×	saturated

Counts

1 → 2

Calls

Call 1

Inputs
(* 2 x)

Outputs
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	36
1	4	36
0	4	36

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 12

Calls

Call 1

Inputs
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)

Outputs
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)

eval2.0ms (0.1%)

Compiler: Compiled 43 to 29 computations (32.6% saved)

prune3.0ms (0.1%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	14	0	14
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	14	5	19

Accuracy

100.0%

Counts

19 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
✓	48.8%	(.f64 #s(literal 2 binary64) (.f64 x x))
✓	4.3%	(*.f64 #s(literal 2 binary64) x)
✓	2.8%	#s(literal 2 binary64)
✓	52.3%	#s(literal -1 binary64)

Compiler

Compiled 40 to 29 computations (27.5% saved)

regimes9.0ms (0.3%)

Counts

5 → 1

Calls

Call 1

Inputs
#s(literal -1 binary64)
#s(literal 2 binary64)
(*.f64 #s(literal 2 binary64) x)
(.f64 #s(literal 2 binary64) (.f64 x x))
(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

Outputs
(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

Calls

4 calls:

3.0ms	(*.f64 x x)
2.0ms	x
1.0ms	(.f64 (.f64 x x) #s(literal 2 binary64))
1.0ms	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`
100.0%	1	`(.f64 (.f64 x x) #s(literal 2 binary64))`
100.0%	1	`(*.f64 x x)`

Compiler

Compiled 20 to 13 computations (35% saved)

regimes7.0ms (0.3%)

Counts

4 → 2

Calls

Call 1

Inputs
#s(literal -1 binary64)
#s(literal 2 binary64)
(*.f64 #s(literal 2 binary64) x)
(.f64 #s(literal 2 binary64) (.f64 x x))

Outputs
#s(literal -1 binary64)
(.f64 #s(literal 2 binary64) (.f64 x x))

Calls

2 calls:

5.0ms	x
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
99.4%	2	`x`
99.4%	2	`(*.f64 x x)`

Compiler

Compiled 6 to 3 computations (50% saved)

regimes3.0ms (0.1%)

Counts

3 → 2

Calls

Call 1

Inputs
#s(literal -1 binary64)
#s(literal 2 binary64)
(*.f64 #s(literal 2 binary64) x)

Outputs
#s(literal -1 binary64)
(*.f64 #s(literal 2 binary64) x)

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
55.1%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0.1%)

Counts

2 → 2

Calls

Call 1

Inputs
#s(literal -1 binary64)
#s(literal 2 binary64)

Outputs
#s(literal -1 binary64)
#s(literal 2 binary64)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
53.9%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal -1 binary64)

Outputs
#s(literal -1 binary64)

Calls

1 calls:

0.0ms

Results

Accuracy	Segments	Branch
52.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	3.1870145103632902e-15	1666.7022593180584

Compiler

Compiled 12 to 9 computations (25% saved)

bsearch13.0ms (0.5%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	5.645364922096082e-8	40.82526496323151

Results

6.0ms

144×

valid

Compiler

Compiled 84 to 72 computations (14.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-mult: 2.0ms (64.3% of total)

ival-sub: 1.0ms (32.2% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch13.0ms (0.5%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	5.645364922096082e-8	40.82526496323151

Results

7.0ms

144×

valid

Compiler

Compiled 66 to 63 computations (4.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-mult: 2.0ms (64.1% of total)

ival-sub: 1.0ms (32% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

soundness1.0ms (0%)

Stop Event

1×

done

Compiler

Compiled 35 to 24 computations (31.4% saved)

preprocess35.0ms (1.4%)

Remove: (abs x)
Compiler: Compiled 134 to 96 computations (28.4% saved)

Numeric.SpecFunctions:logGammaCorrection from math-functions-0.1.5.2

analyze0.0ms (0%)

sample644.0ms (25.4%)

preprocess17.0ms (0.7%)

explain61.0ms (2.4%)

eval0.0ms (0%)

prune1.0ms (0%)

localize37.0ms (1.5%)

series4.0ms (0.2%)

rewrite824.0ms (32.5%)

simplify324.0ms (12.8%)

eval102.0ms (4%)

prune85.0ms (3.4%)

localize36.0ms (1.4%)

series2.0ms (0.1%)

rewrite250.0ms (9.8%)

simplify6.0ms (0.2%)

eval3.0ms (0.1%)

prune13.0ms (0.5%)

localize23.0ms (0.9%)

series3.0ms (0.1%)

rewrite8.0ms (0.3%)

simplify3.0ms (0.1%)

eval2.0ms (0.1%)

prune3.0ms (0.1%)

regimes9.0ms (0.3%)

regimes7.0ms (0.3%)

regimes3.0ms (0.1%)

regimes2.0ms (0.1%)

regimes1.0ms (0%)

bsearch0.0ms (0%)

bsearch13.0ms (0.5%)

bsearch13.0ms (0.5%)

soundness1.0ms (0%)

preprocess35.0ms (1.4%)

end0.0ms (0%)

Profiling